A note on zero-sets of fractional sobolev functions with negative power of integrability

Schikorra, Armin

doi:10.1090/S0002-9939-2014-12372-0

A note on zero-sets of fractional sobolev functions with negative power of integrability
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by Armin Schikorra PDF

Proc. Amer. Math. Soc. 143 (2015), 1189-1197 Request permission

Abstract:

We extend a Poincaré-type inequality for functions with large zero-sets by Jiang and Lin to fractional Sobolev spaces. As a consequence, we obtain a Hausdorff dimension estimate on the size of zero-sets for fractional Sobolev functions whose inverse is integrable. Also, for a suboptimal Hausdorff dimension estimate, we give a completely elementary proof based on a pointwise Poincaré-style inequality.

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